Techniques of robust inverse design that account for manufacturing variabilities due to operating conditions

ABSTRACT

Embodiments of techniques for inverse design of physical devices are described herein, in the context of generating designs for photonic integrated circuits (including a multi-channel photonic demultiplexer). In some embodiments, an initial design of the physical device is received, and a plurality of sets of operating conditions for fabrication of the physical device are determined. In some embodiments, the performance of the physical device as fabricated under the sets of operating conditions is simulated, and a total performance loss value is backpropagated to determine a gradient to be used to update the initial design. In some embodiments, instead of simulating fabrication of the physical device under the sets of operating conditions, a robustness loss is determined and combined with the performance loss to determine the gradient.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.16/796,660, filed Feb. 20, 2020, the entire disclosure of which ishereby incorporated by reference herein for all purposes.

TECHNICAL FIELD

This disclosure relates generally to photonic devices, and in particularbut not exclusively, relates to optical multiplexers and demultiplexers.

BACKGROUND INFORMATION

Fiber-optic communication is typically employed to transmit informationfrom one place to another via light that has been modulated to carry theinformation. For example, many telecommunication companies use opticalfiber to transmit telephone signals, internet communication, and cabletelevision signals. But the cost of deploying optical fibers forfiber-optic communication may be prohibitive. As such, techniques havebeen developed to more efficiently use the bandwidth available within asingle optical fiber. Wavelength-division multiplexing is one suchtechnique that bundles multiple optical carrier signals onto a singleoptical fiber using different wavelengths.

SUMMARY

In some embodiments, a non-transitory computer-readable medium isprovided. The medium has logic stored thereon that, in response toexecution by at least one computing device, causes the at least onecomputing device to perform actions for generating a design of aphysical device, the actions comprising receiving an initial design ofthe physical device; simulating performance of the physical device usingthe initial design to determine a performance loss value; determining arobustness loss value that represents an effect of perturbations inoperating conditions during fabrication on the performance loss value;determining a total performance loss value based on the performance lossvalue and the robustness loss value; backpropagating the totalperformance loss value to determine a gradient corresponding to aninfluence of changes in the initial design on the total performance lossvalue; and revising the initial design of the physical device based atleast in part on the gradient.

In some embodiments, a system comprising at least one computing deviceis provided. The computing device is configured with logic that, inresponse to execution by the at least one computing device, cause thesystem to perform actions for generating a design of a physical device,the actions comprising receiving an initial design of the physicaldevice; simulating performance of the physical device using the initialdesign to determine a performance loss value; determining a robustnessloss value that represents an effect of perturbations in operatingconditions during fabrication on the performance loss value; determininga total performance loss value based on the performance loss value andthe robustness loss value; backpropagating the total performance lossvalue to determine a gradient corresponding to an influence of changesin the initial design on the total performance loss value; and revisingthe initial design of the physical device based at least in part on thegradient.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting and non-exhaustive embodiments of the invention aredescribed with reference to the following figures, wherein likereference numerals refer to like parts throughout the various viewsunless otherwise specified. Not all instances of an element arenecessarily labeled so as not to clutter the drawings where appropriate.The drawings are not necessarily to scale, emphasis instead being placedupon illustrating the principles being described.

FIG. 1 is a functional block diagram illustrating a system for opticalcommunication between two optical communication devices via an opticalsignal, in accordance with an embodiment of the present disclosure.

FIG. 2A and FIG. 2B respectively illustrate an example demultiplexer andmultiplexer, in accordance with an embodiment of the present disclosure.

FIG. 2C illustrates an example distinct wavelength channel of amulti-channel optical signal, in accordance with an embodiment of thepresent disclosure.

FIG. 3A-FIG. 3D illustrate different views of an example photonicdemultiplexer, in accordance with an embodiment of the presentdisclosure.

FIG. 4A and FIG. 4B illustrate a more detailed cross-sectional view of adispersive region of an example photonic demultiplexer, in accordancewith an embodiment of the present disclosure.

FIG. 5 is a functional block diagram illustrating a system forgenerating a design of a photonic integrated circuit, in accordance withan embodiment of the present disclosure.

FIG. 6A illustrates a demonstrative simulated environment describing aphotonic integrated circuit, in accordance with an embodiment of thepresent disclosure.

FIG. 6B illustrates an example operational simulation of a photonicintegrated circuit, in accordance with an embodiment of the presentdisclosure.

FIG. 6C illustrates an example adjoint simulation within the simulatedenvironment by backpropagating a loss value, in accordance with anembodiment of the present disclosure.

FIG. 7A is a flow chart illustrating example time steps for anoperational simulation and an adjoint simulation, in accordance withvarious aspects of the present disclosure.

FIG. 7B is a chart illustrating the relationship between the updateoperation for the operational simulation and the adjoint simulation(e.g., backpropagation), in accordance with an embodiment of the presentdisclosure.

FIG. 8 is a flowchart that illustrates a non-limiting example embodimentof a method for generating a design of physical device such as aphotonic integrated circuit, in accordance with various aspects of thepresent disclosure.

FIG. 9 is a flow chart illustrating example time steps for anoperational simulation and an adjoint simulation, in accordance withvarious aspects of the present disclosure.

FIG. 10 is a flowchart that illustrates a non-limiting exampleembodiment of a method of optimizing a design of a physical deviceaccording to various aspects of the present disclosure.

DETAILED DESCRIPTION

Embodiments of techniques for inverse design of physical devices aredescribed herein, in the context of generating designs for photonicintegrated circuits (including a multi-channel photonic demultiplexer).In the following description numerous specific details are set forth toprovide a thorough understanding of the embodiments. One skilled in therelevant art will recognize, however, that the techniques describedherein can be practiced without one or more of the specific details, orwith other methods, components, materials, etc. In other instances,well-known structures, materials, or operations are not shown ordescribed in detail to avoid obscuring certain aspects.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the present invention. Thus, theappearances of the phrases “in one embodiment” or “in an embodiment” invarious places throughout this specification are not necessarily allreferring to the same embodiment. Furthermore, the particular features,structures, or characteristics may be combined in any suitable manner inone or more embodiments.

Wavelength division multiplexing and its variants (e.g., densewavelength division multiplexing, coarse wavelength divisionmultiplexing, and the like) take advantage of the bandwidth of opticalfibers by bundling multiple optical carrier signals onto a singleoptical fiber. Once the multiple carrier signals are bundled together,they are transmitted from one place to another over the single opticalfiber where they may be demultiplexed to be read out by an opticalcommunication device. However, devices that decouple the carrier signalsfrom one another remain prohibitive in terms of cost, size, and thelike.

Moreover, design of photonic devices, such as those used for opticalcommunication, are traditionally designed via conventional techniquessometimes determined through a simple guess and check method ormanually-guided grid-search in which a small number of design parametersfrom pre-determined designs or building blocks are adjusted forsuitability to a particular application. However, in actuality, thesedevices may have design parameters ranging from hundreds all the way tomany billions or more, dependent on the device size and functionality.Thus, as functionality of photonic devices increases and manufacturingtolerances improve to allow for smaller device feature sizes, it becomesincreasingly important to take full advantage of these improvements viaoptimized device design.

Described herein are embodiments of a photonic integrated circuit (e.g.,a multi-channel photonic demultiplexer and/or multiplexer) having adesign obtainable by an inverse design process. More specifically,techniques described in embodiments herein utilize gradient-basedoptimization in combination with first-principle simulations to generatea design from an understanding of the underlying physics that areexpected to govern the operation of the photonic integrated circuit. Itis appreciated in other embodiments, design optimization of photonicintegrated circuits without gradient-based techniques may also be used.Advantageously, embodiments and techniques described herein are notlimited to conventional techniques used for design of photonic devices,in which a small number of design parameters for pre-determined buildingblocks are adjusted based on suitability to a particular application.Rather, the first-principles based designs described herein are notnecessarily dependent on human intuition and generally may result indesigns which outstrip current state-of-the-art designs in performance,size, robustness, or a combination thereof. Further still, rather thanbeing limited to a small number of design parameters due to conventionaltechniques, the embodiments and techniques described herein may providescalable optimization of a nearly unlimited number of design parameters.It will also be appreciated that, though the design and fabrication ofphotonic integrated circuits is described throughout the present text,similar inverse design techniques may be used to generate designs forother types of physical devices.

FIG. 1 is a functional block diagram illustrating a system 100 foroptical communication (e.g., via wavelength division multiplexing orother techniques) between optical communication device 102 and opticalcommunication device 120 via optical signal 110, in accordance withvarious aspects of the present disclosure. More generally, opticalcommunication device 102 is configured to transmit information bymodulating light from one or more light sources into a multi-channeloptical signal 110 (e.g., a singular optical signal that includes aplurality of distinct wavelength channels) that is subsequentlytransmitted from optical communication device 102 to opticalcommunication device 120 via an optical fiber, a light guide, a waveguide, or other photonic device. Optical communication device 120receives the multi-channel optical signal 110 and demultiplexes each ofthe plurality of distinct wavelength channels from the multi-channeloptical signal 110 to extract the transmitted information. It isappreciated that in some embodiments optical communication device 102and optical communication device 120 may be distinct and separatedevices (e.g., an optical transceiver or transmitter communicativelycoupled via one or more optical fibers to a separate optical transceiveror receiver). However, in other embodiments, optical communicationdevice 102 and optical communication device 120 may be part of asingular component or device (e.g., a smartphone, a tablet, a computer,optical device, or the like). For example, optical communication device102 and optical communication device 120 may both be constituentcomponents on a monolithic integrated circuit that are coupled to oneanother via a waveguide that is embedded within the monolithicintegrated circuit and is adapted to carry optical signal 110 betweenoptical communication device 102 and optical communication device 120 orotherwise transmit the optical signal between one place and another.

In the illustrated embodiment, optical communication device 102 includesa controller 104, one or more interface device(s) 112 (e.g., fiber opticcouplers, light guides, waveguides, and the like), a multiplexer (mux),demultiplexer (demux), or combination thereof (MUX/DEMUX 114), one ormore light source(s) 116 (e.g., light emitting diodes, lasers, and thelike), and one or more light sensor(s) 118 (e.g., photodiodes,phototransistors, photoresistors, and the like) coupled to one another.The controller includes one or more processor(s) 106 (e.g., one or morecentral processing units, application specific circuits, fieldprogrammable gate arrays, or otherwise) and memory 108 (e.g., volatilememory such as DRAM and SAM, non-volatile memory such as ROM, flashmemory, and the like). It is appreciated that optical communicationdevice 120 may include the same or similar elements as opticalcommunication device 102, which have been omitted for clarity.

Controller 104 orchestrates operation of optical communication device102 for transmitting and/or receiving optical signal 110 (e.g., amulti-channel optical signal having a plurality of distinct wavelengthchannels or otherwise). Controller 104 includes software (e.g.,instructions included in memory 108 coupled to processor 106) and/orhardware logic (e.g., application specific integrated circuits,field-programmable gate arrays, and the like) that when executed bycontroller 104 causes controller 104 and/or optical communication device102 to perform operations.

In one embodiment, controller 104 may choreograph operations of opticalcommunication device 102 to cause light source(s) 116 to generate aplurality of distinct wavelength channels that are multiplexed viaMUX/DEMUX 114 into a multi-channel optical signal 110 that issubsequently transmitted to optical communication device 120 viainterface device 112. In other words, light source(s) 116 may outputlight having different wavelengths (e.g., 1271 nm, 1291 nm, 1311 nm,1331 nm, 1506 nm, 1514 nm, 1551 nm, 1571, or otherwise) that may bemodulated or pulsed via controller 104 to generate a plurality ofdistinct wavelength channels representative of information. Theplurality of distinct wavelength channels are subsequently combined orotherwise multiplexed via MUX/DEMUX 114 into a multi-channel opticalsignal 110 that is transmitted to optical communication device 120 viainterface device 112. In the same or another embodiment, controller 104may choreograph operations of optical communication device 102 to causea plurality of distinct wavelength channels to be demultiplexed viaMUX/DEMUX 114 from a multi-channel optical signal 110 that is receivedvia interface device 112 from optical communication device 120.

It is appreciated that in some embodiments certain elements of opticalcommunication device 102 and/or optical communication device 120 mayhave been omitted to avoid obscuring certain aspects of the disclosure.For example, optical communication device 102 and optical communicationdevice 120 may include amplification circuitry, lenses, or components tofacilitate transmitting and receiving optical signal 110. It is furtherappreciated that in some embodiments optical communication device 102and/or optical communication device 120 may not necessarily include allelements illustrated in FIG. 1. For example, in one embodiment opticalcommunication device 102 and/or optical communication device 120 arepassive devices that operate as an intermediary device that maypassively multiplex a plurality of distinct wavelength channels into amulti-channel optical signal 110 and/or demultiplex a plurality ofdistinct wavelength channels from a multi-channel optical signal 110.

FIG. 2A and FIG. 2B respectively illustrate an example demultiplexer 206and multiplexer 208, in accordance with various aspects of the presentdisclosure. Demultiplexer 206 and multiplexer 208 are possibleembodiments of MUX/DEMUX 114 illustrated in FIG. 1, and which may bepart of an integrated photonic circuit, silicon photonic device, orotherwise

As illustrated in FIG. 2A, demultiplexer 206 includes an input region202 and a plurality of output regions 204. Demultiplexer 206 isconfigured to receive a multi-channel optical signal 110 that includes aplurality of distinct wavelength channels (e.g., Ch. 1, Ch. 2, Ch. 3, .. . Ch. N, each having a center wavelength respectively corresponding toλ₁, λ₂, λ₃, . . . λ_(N)) via input region 202 (e.g., a waveguide thatmay correspond to interface device 112 illustrated in FIG. 1) tooptically separate each of the plurality of distinct wavelength channelsfrom the multi-channel optical signal 110 and respectively guide each ofthe plurality of distinct wavelength channels to a corresponding one ofa plurality of output regions 204 (e.g., a plurality of waveguides thatmay correspond to interface device(s) 112 illustrated in FIG. 1). Morespecifically, in the illustrated embodiment, each of the output regions204 receives a portion of the multi-channel optical signal thatcorresponds to, or is otherwise representative of, one of the pluralityof distinct wavelength channels that may be output as plurality ofoptical signals (e.g., λ₁, λ₂, λ₃, . . . λ_(N)). The plurality of outputregions 204 may each be coupled to a respective light sensor (e.g.,corresponding to light sensor 118 illustrated in FIG. 1), which may beutilized to convert the optical signals demultiplexed from themulti-channel optical signal 110 into electrical signals for furtherprocessing.

In the illustrated embodiment of FIG. 2B, multiplexer 208 includes aplurality of input regions 216 and an output region 210. Multiplexer isconfigured to receive a plurality of distinct optical signals (e.g., λ₁,λ₂, λ₃, . . . λ_(N)), each at a respective one of the plurality of inputregions 216 (e.g., a plurality of waveguides that may correspond tointerface device(s) 112 illustrated in FIG. 1). Multiplexer 208 isstructured or otherwise configured to optically combine (i.e.,multiplex) each of the plurality of distinct wavelength channels into amulti-channel optical signal 110 that is guided to output region 210(e.g., a waveguide that may correspond to interface device 112illustrated in FIG. 1). It is appreciated that in some embodiments,demultiplexer 206 illustrated in FIG. 2A and multiplexer 208 illustratedin FIG. 2B may be bidirectional such that each device may function asboth a demultiplexer and multiplexer.

FIG. 2C illustrates an example distinct wavelength channel of amulti-channel optical signal (e.g., Ch. N is multi-channel opticalsignal 110 illustrated in FIG. 1, FIG. 2A, and FIG. 2B), in accordancewith various aspects of the present disclosure. The example channel maybe representative of an individual channel included in a plurality ofdistinct wavelength channels of the multi-channel optical signal thatmay be demultiplexed and/or multiplexed by demultiplexer 206 of FIG. 2Aand/or multiplexer 208 of FIG. 2B. Each of the distinct wavelengthchannels may have different center wavelengths (λ_(N)) including atleast one of 1271 nm, 1291 nm, 1311 nm, 1331 nm, 1506 nm, 1514 nm, 1551nm, or 1571 nm, or otherwise. In the illustrated embodiment of FIG. 2C,the distinct wavelength channel has a channel bandwidth 212 ofapproximately 13 nm wide. However, in other embodiments the channelbandwidth may be different than 13 nm wide. Rather, the channelbandwidth may be considered a configurable parameter that is dependentupon the structure of MUX/DEMUX 114 of FIG. 1, demultiplexer 206 of FIG.2A, and/or multiplexer 208 of FIG. 2B. For example, in some embodimentseach of the plurality of distinct wavelength channels may share a commonbandwidth that may correspond to 13 nm or otherwise. Referring back toFIG. 2C, the channel bandwidth 212 may be defined as the width of apassband region 218 (i.e., the region defined as being between PB₁ andPB₂). The passband region 218 may represent an approximate powertransmission of a demultiplexer or multiplexer. It is appreciated thatin some embodiments the passband region 218 may include ripple asillustrated in FIG. 2C, which corresponds to fluctuations within thepassband region 218. In one or more embodiments, the ripple within thepassband region around a central value 214 may be +/−2 dB or less, +/−1dB or less, +/−0.5 dB or less, or otherwise. In some embodiments, thechannel bandwidth 212 may be defined by the passband region 218. Inother embodiments, the channel bandwidth 212 may be defined as themeasured power above a threshold (e.g., dB_(th)). For example,demultiplexer 206 illustrated in FIG. 2A may optically separate channelN from multi-channel optical signal 110 and have a corresponding channelbandwidth for channel N equivalent to the range of wavelengths above athreshold value that are transmitted to the output region 204 mapped tochannel N (i.e., λ_(N)). In the same or other embodiments, isolation ofthe channel (i.e., defined by channel bandwidth 212) may also beconsidered when optimizing the design. The isolation may be defined as aratio between the passband region 218 and the stopband regions (e.g.,regions less than SB₁ and greater than SB₂). It is further appreciatedthat transition band regions (e.g., a first transition region betweenSB₁ and PB₁ and a second transition region between PB₂ and SB₂) areexemplary and may be exaggerated for the purposes of illustration. Insome embodiments, optimization of the design of the photonicdemultiplexer may also include a target metric for a slope, width, orthe like of the transition band regions.

FIG. 3A-FIG. 3D illustrate different views of an example photonicdemultiplexer, in accordance with an embodiment of the presentdisclosure. Photonic demultiplexer 316 is one possible implementation ofMUX/DEMUX 114 illustrated in FIG. 1 and demultiplexer 206 illustrated inFIG. 2A. It is further appreciated that while discussion henceforth maybe directed towards photonic integrated circuits capable ofdemultiplexing a plurality of distinct wavelength channels from amulti-channel optical signal, that in other embodiments, a demultiplexer(e.g., demultiplexer 316) may also or alternatively be capable ofmultiplexing a plurality of distinct wavelength channels into amulti-channel optical signal, in accordance with embodiments of thepresent disclosure.

FIG. 3A illustrates a cross-sectional view of demultiplexer 316 along alateral plane within an active layer defined by a width 320 and a length322 of the demultiplexer 316. As illustrated, demultiplexer 316 includesan input region 302 (e.g., comparable to input region 202 illustrated inFIG. 2A), a plurality of output regions 304 (e.g., comparable toplurality of output regions 204 illustrated in FIG. 2A), and adispersive region optically disposed between the input region 302 andplurality of output regions 304. The input region 302 and plurality ofoutput regions 304 (e.g., output region 308, output region 310, outputregion 312, and output region 314) may each be waveguides (e.g., slabwaveguide, strip waveguide, slot waveguide, or the like) capable ofpropagating light along the path of the waveguide. The dispersive region332 includes a first material and a second material (see, e.g., FIG. 3D)inhomogeneously interspersed to form a plurality of interfaces that eachcorrespond to a change in refractive index of the dispersive region 332and collectively structure the dispersive region 332 to opticallyseparate each of a plurality of distinct wavelength channels (e.g., Ch.1, Ch. 2, Ch. 3, . . . Ch. N illustrated in FIG. 2A) from amulti-channel optical signal (e.g., optical signal 110 illustrated inFIG. 2A) and respectively guide each of the plurality of distinctwavelength channels to a corresponding one of the plurality of outputregions 304 when the input region 302 receives the multi-channel opticalsignal. In other words, input region 302 is adapted to receive themulti-channel optical signal including a plurality of distinctwavelength channels and the plurality of output regions 304 are adaptedto each receive a corresponding one of the plurality of distinctwavelength channels demultiplexed from the multi-channel optical signalvia dispersive region 332.

As illustrated in FIG. 3A, and more clearly shown in FIG. 3D and FIG.4A-B, the shape and arrangement of the first and second material thatare inhomogeneously interspersed create a plurality of interfaces thatcollectively form a material interface pattern along a cross-sectionalarea of dispersive region 332 that is at least partially surrounded by aperiphery boundary region 318 that includes the second material. In someembodiments periphery region 318 has a substantially homogeneouscomposition that includes the second material. In the illustratedembodiment, dispersive region 332 includes a first side 328 and a secondside 330 that each interface with an inner boundary (i.e., the unlabeleddashed line of periphery region 318 disposed between dispersive region332 and dashed-dotted line corresponding to an outer boundary ofperiphery region 318). First side 328 and second side 330 are disposedcorrespond to opposing sides of dispersive region 332. Input region 302is disposed proximate to first side 328 (e.g., one side of input region302 abuts first side 328 of dispersive region 332) while each of theplurality of output regions 304 are disposed proximate to second side330 (e.g., one side of each of the plurality of output regions 304 abutssecond side 330 of dispersive region 332).

In the illustrated embodiment each of the plurality of output regions304 are parallel to each other one of the plurality of output regions304. However, in other embodiments the plurality of output regions 304may not be parallel to one another or even disposed on the same side(e.g., one or more of the plurality of output regions 304 and/or inputregion 302 may be disposed proximate to sides of dispersive region 332that are adjacent to first side 328 and/or second side 330). In someembodiments adjacent ones of the plurality of output regions areseparated from each other by a common separation distance when theplurality of output regions includes at least three output regions. Forexample, as illustrated adjacent output region 308 and output region 310are separated from one another by distance 306, which may be common tothe separation distance between other pairs of adjacent output regions.

As illustrated in the embodiment of FIG. 3A, demultiplexer 316 includesfour output regions 304 (e.g., output region 308, output region 310,output region 312, output region 314) that are each respectively mapped(i.e., by virtue of the structure of dispersive region 332) to arespective one of four channels included in a plurality of distinctwavelength channels. More specifically, the plurality of interfaces ofdispersive region 332, defined by the inhomogeneous interspersion of afirst material and a second material, form a material interface patternalong a cross-sectional area of the dispersive region 332 (e.g., asillustrated in FIG. 3A, FIG. 4A, or FIG. 4B) to cause the dispersiveregion 332 to optically separate each of the four channels from themulti-channel optical signal and route each of the four channels to arespective one of the four output regions 304 when the input region 302regions the multi-channel optical signal.

It is noted that the first material and second material of dispersiveregion 332 are arranged and shaped within the dispersive region suchthat the material interface pattern is substantially proportional to adesign obtainable with an inverse design process, which will bediscussed in greater detail later in the present disclosure. Morespecifically, in some embodiments, the inverse design process mayinclude iterative gradient-based optimization of a design based at leastin part on a loss function that incorporates a performance loss (e.g.,to enforce functionality) and a fabrication loss (e.g., to enforcefabric ability and binarization of a first material and a secondmaterial) that is reduced or otherwise adjusted via iterativegradient-based optimization to generate the design. In the same or otherembodiment, other optimization techniques may be used instead of, orjointly with, gradient-based optimization. Advantageously, this allowsfor optimization of a near unlimited number of design parameters toachieve functionality and performance within a predetermined area thatmay not have been possible with conventional design techniques.

For example, in one embodiment dispersive region 332 is structured tooptically separate each of the four channels from the multi-channeloptical signal within a predetermined area of 35 μm×35 μm (e.g., asdefined by width 324 and length 326 of dispersive region 332) when theinput region 302 receives the multi-channel optical signal. In the sameor another embodiment, the dispersive region is structured toaccommodate a common bandwidth for each of the four channels, each ofthe four channels having different center wavelengths. In one embodimentthe common bandwidth is approximately 13 nm wide and the differentcenter wavelengths is selected from a group consisting of 1271 nm, 1291nm, 1311 nm, 1331 nm, 1506 nm, 1514 nm, 1551 nm, and 1571 nm. In someembodiments, the entire structure of demultiplexer 316 (e.g., includinginput region 302, periphery region 318, dispersive region 332, andplurality of output regions 304) fits within a predetermined area (e.g.,as defined by width 320 and length 322). In one embodiment thepredetermined area is 35 μm×35 μm. It is appreciated that in otherembodiments dispersive region 332 and/or demultiplexer 316 fits withinother areas greater than or less than 35 μm×35 μm, which may result inchanges to the structure of dispersive region 332 (e.g., the arrangementand shape of the first and second material) and/or other components ofdemultiplexer 316.

In the same or other embodiments the dispersive region is structured tohave a power transmission of −2 dB or greater from the input region 302,through the dispersive region 332, and to the corresponding one of theplurality of output regions 304 for a given wavelength within one of theplurality of distinct wavelength channels. For example, if channel 1 ofa multi-channel optical signal is mapped to output region 308, then whendemultiplexer 316 receives the multi-channel optical signal at inputregion 302 the dispersive region 332 will optically separate channel 1from the multi-channel optical signal and guide a portion of themulti-channel optical signal corresponding to channel 1 to output region308 with a power transmission of −2 dB or greater. In the same oranother embodiment, dispersive region 332 is structured such that anadverse power transmission (i.e., isolation) for the given wavelengthfrom the input region to any of the plurality of output regions otherthan the corresponding one of the plurality of output regions is −30 dBor less, −22 dB or less, or otherwise. For example, if channel 1 of amulti-channel optical signal is mapped to output region 308, then theadverse power transmission from input region 302 to any other one of theplurality of output regions (e.g., output region 310, output region 312,output region 314) other than the corresponding one of the plurality ofoutput regions (e.g., output region 308) is −30 dB or less, −22 dB orless, or otherwise. In some embodiments, a maximum power reflection fromdemultiplexer 316 of an input signal (e.g., a multi-channel opticalsignal) received at an input region (e.g., input region 302) isreflected back to the input region by dispersive region 332 or otherwiseis −40 dB or less, −20 dB or less, −8 dB or less, or otherwise. It isappreciated that in other embodiments the power transmission, adversepower transmission, maximum power, or other performance characteristicsmay be different than the respective values discussed herein, but thestructure of dispersive region 332 may change due to the intrinsicrelationship between structure, functionality, and performance ofdemultiplexer 316.

FIG. 3B illustrates a vertical schematic or stack of various layers thatare included in the illustrated embodiment of demultiplexer 316.However, it is appreciated that the illustrated embodiment is notexhaustive and that certain features or elements may be omitted to avoidobscuring certain aspects of the invention. In the illustratedembodiment, demultiplexer 316 includes substrate 334, dielectric layer336, active layer 338 (e.g., as shown in the cross-sectionalillustration of FIG. 3A), and a cladding layer 340. In some embodiments,demultiplexer 316 may be, in part or otherwise, a photonic integratedcircuit or silicon photonic device that is compatible with conventionalfabrication techniques (e.g., lithographic techniques such asphotolithographic, electron-beam lithography and the like, sputtering,thermal evaporation, physical and chemical vapor deposition, and thelike).

In one embodiment a silicon on insulator (SOI) wafer may be initiallyprovided that includes a support substrate (e.g., a silicon substrate)that corresponds to substrate 334, a silicon dioxide dielectric layerthat corresponds to dielectric layer 336, a silicon layer (e.g.,intrinsic, doped, or otherwise), and a oxide layer (e.g., intrinsic,grown, or otherwise). In one embodiment, the silicon in the active layer338 may be etched selectively by lithographically creating a pattern onthe SOI wafer that is transferred to SOI wafer via a dry etch process(e.g., via a photoresist mask or other hard mask) to remove portions ofthe silicon. The silicon may be etched all the way down to dielectriclayer 336 to form voids that may subsequently be backfilled with silicondioxide that is subsequently encapsulated with silicon dioxide to formcladding layer 340. In one embodiment, there may be several etch depthsincluding a full etch depth of the silicon to obtain the targetedstructure. In one embodiment, the silicon may be 206 nm thick and thusthe full etch depth may be 206 nm. In some embodiments, this may be atwo-step encapsulation process in which two silicon dioxide depositionsare performed with an intermediate chemical mechanical planarizationused to yield a planar surface.

FIG. 3C illustrates a more detailed view of active layer 338 (relativeto FIG. 3B) taken along a portion of periphery region 318 that includesinput region 302 of FIG. 3A. In the illustrated embodiment, active layer338 includes a first material 342 with a refractive index of ε₁ and asecond material 344 with a refractive index of ε₂ that is different fromε₁. Homogenous regions of the first material 342 and the second material344 may form waveguides or portions of waveguides that correspond toinput region 302 and plurality of output regions 304 as illustrated inFIG. 3A and FIG. 3C.

FIG. 3D illustrates a more detailed view of active layer 338 (relativeto FIG. 3B) taken along dispersive region 332. As described previously,active layer 338 includes a first material 342 (e.g., silicon) and asecond material 344 (e.g., silicon dioxide) that are inhomogeneouslyinterspersed to form a plurality of interfaces 346 that collectivelyform a material interface pattern. Each of the plurality of interfaces346 that form the interface pattern correspond to a change in refractiveindex of dispersive region 332 to structure the dispersive region (i.e.,the shape and arrangement of first material 342 and second material 344)to provide, at least in part, the functionality of demultiplexer 316(i.e., optical separation of the plurality of distinct wavelengthchannels from the multi-channel optical signal and respective guidanceof each of the plurality of distinct wavelength channels to thecorresponding one of the plurality of output regions 304 when the inputregion 302 receives the multi-channel optical signal).

It is appreciated that in the illustrated embodiments of demultiplexer316 as shown in FIG. 3A-D, the change in refractive index is shown asbeing vertically consistent (i.e., the first material 342 and secondmaterial 344 form interfaces that are substantially vertical orperpendicular to a lateral plane or cross-section of demultiplexer 316.However, in the same or other embodiments, the plurality of interfaces(e.g., interfaces 346 illustrated in FIG. 3D) may not be substantiallyperpendicular with the lateral plane or cross-section of demultiplexer316.

FIG. 4A illustrates a more detailed cross-sectional view of a dispersiveregion of example photonic demultiplexer 400, in accordance with anembodiment of the present disclosure. FIG. 4B illustrates a moredetailed view of an interface pattern formed by the shape andarrangement of a first material 410 and a second material 412 for thedispersive region of the photonic demultiplexer 400 of FIG. 4A. Photonicdemultiplexer 400 is one possible implementation of MUX/DEMUX 114illustrated in FIG. 1, demultiplexer 206 illustrated in FIG. 2A, anddemultiplexer 316 illustrated in FIG. 3A-D.

As illustrated in FIG. 4A and FIG. 4B, photonic demultiplexer 400includes an input region 402, a plurality of output regions 404, and adispersive region 406 optically disposed between input region 402 andplurality of output regions 404. Dispersive region 406 is surrounded, atleast in part, by a peripheral region 408 that includes an innerboundary 414 and an outer boundary 416. It is appreciated that likenamed or labeled elements of photonic demultiplexer 400 may similarlycorrespond to like named or labeled elements of other demultiplexersdescribed in embodiments of the present disclosure.

The first material 410 (i.e., black colored regions within dispersiveregion 406) and second material 412 (i.e., white colored regions withindispersive region 406) of photonic demultiplexer 400 are inhomogeneouslyinterspersed to create a plurality of interfaces that collectively formmaterial interface pattern 420 as illustrated in FIG. 4B. Morespecifically, an inverse design process that utilizes iterativegradient-based optimization, Markov Chain Monte Carlo optimization, orother optimization techniques combined with first principles simulationsto generate a design that is substantially replicated by dispersiveregion 406 within a proportional or scaled manner such that photonicdemultiplexer 400 provides the desired functionality. In the illustratedembodiment, dispersive region 406 is structured to optically separateeach of a plurality of distinct wavelength channels from a multi-channeloptical signal and respectively guide each of the plurality of distinctwavelength channels to a corresponding one of the plurality of outputregions 404 when the input region 402 receives the multi-channel opticalsignal. More specifically, the plurality of output regions 404-A, -B,-C, and -D are respectively mapped to wavelength channels having centerwavelengths correspond to 1271 nm, 1291 nm, 1311 nm, and 1331 nm. Inanother embodiment, output regions 404-A, 404-B, 404-C, and 404-D arerespectfully mapped to wavelength channels having center wavelengthsthat correspond to 1506 nm, 1514 nm, 1551 nm, and 1571 nm.

As illustrated in FIG. 4B, material interface pattern 420, which isdefined by the black lines within dispersive region 406 and correspondsto a change in refractive index within dispersive region 406, includes aplurality of protrusions 422. A first protrusion 422-A is formed of thefirst material 410 and extends from peripheral region 408 intodispersive region 406. Similarly, a second protrusion 422-B is formed ofthe second material 412 and extends from peripheral region 408 intodispersive region 406. Further illustrated in FIG. 4B, dispersive region406 includes a plurality of islands 424 formed of either the firstmaterial 410 or the second material 412. The plurality of islands 424include a first island 424-A that is formed of the first material 410and is surrounded by the second material 412. The plurality of islands424 also includes a second island 424-B that is formed of the secondmaterial 412 and is surrounded by the first material 412.

In some embodiments, material interface pattern 420 includes one or moredendritic shapes, wherein each of the one or more dendritic shapes aredefined as a branched structure formed from first material 410 or secondmaterial 412 and having a width that alternates between increasing anddecreasing in size along a corresponding direction. Referring back toFIG. 4A, for clarity, dendritic structure 418 is labeled with a whitearrow having a black border. As can be seen, the width of dendriticstructure 418 alternatively increases and decreases in size along acorresponding direction (i.e., the white labeled arrow overlaying alength of dendritic structure 418) to create a branched structure. It isappreciated that in other embodiments there may be no protrusions, theremay be no islands, there may be no dendritic structures, or there may beany number, including zero, of protrusions, islands of any materialincluded in the dispersive region 406, dendritic structures, or acombination thereof.

In some embodiments, the inverse design process includes a fabricationloss that enforces a minimum feature size, for example, to ensurefabricability of the design. In the illustrated embodiment of photonicdemultiplexer 400 illustrated in FIG. 4A and FIG. 4B, material interfacepattern 420 is shaped to enforce a minimum feature size withindispersive region 406 such that the plurality of interfaces within thecross-sectional area formed with first material 410 and second material412 do not have a radius of curvature with a magnitude of less than athreshold size. For example, if the minimum feature size is 150 nm, theradius of curvature for any of the plurality of interfaces have amagnitude of less than the threshold size, which corresponds the inverseof half the minimum feature size (i.e., 1/75 nm⁻¹). Enforcement of sucha minimum feature size prevents the inverse design process fromgenerating designs that are not fabricable by considering manufacturingconstraints, limitations, and/or yield. In the same or otherembodiments, different or additional checks on metrics related tofabricability may be utilized to enforce a minimum width or spacing as aminimum feature size.

FIG. 5 is a functional block diagram illustrating a system 500 forgenerating a design of a photonic integrated circuit (i.e., photonicdevice), in accordance with an embodiment of the disclosure. System 500may be utilized to perform an inverse design process that generates adesign with iterative gradient-based optimization that takes intoconsideration the underlying physics that govern the operation of thephotonic integrated circuit. More specifically, system 500 is a designtool that may be utilized to optimize structural parameters (e.g., shapeand arrangement of a first material and a second material within thedispersive region of the embodiments described in the presentdisclosure) of photonic integrated circuits based on first-principlessimulations (e.g., electromagnetic simulations to determine a fieldresponse of the photonic device to an excitation source) and iterativegradient-based optimization. In other words, system 500 may provide adesign obtained via the inverse design process that is substantiallyreplicated (i.e., proportionally scaled) by dispersive region 332 anddispersive region 406 of demultiplexer 316 and photonic demultiplexer400 illustrated in FIG. 3A and FIG. 4A, respectively.

As illustrated, system 500 includes controller 512, display 502, inputdevice(s) 504, communication device(s) 506, network 508, remoteresources 510, bus 534, and bus 520. Controller 512 includes processor514, memory 516, local storage 518, and photonic device simulator 522.Photonic device simulator 522 includes operational simulation engine526, fabrication loss calculation logic 528, calculation logic 524,adjoint simulation engine 530, and optimization engine 532. It isappreciated that in some embodiments, controller 512 may be adistributed system.

Controller 512 is coupled to display 502 (e.g., a light emitting diodedisplay, a liquid crystal display, and the like) coupled to bus 534through bus 520 for displaying information to a user utilizing system500 to optimize structural parameters of the photonic device (i.e.,demultiplexer). Input device 504 is coupled to bus 534 through bus 520for communicating information and command selections to processor 514.Input device 504 may include a mouse, trackball, keyboard, stylus, orother computer peripheral, to facilitate an interaction between the userand controller 512. In response, controller 512 may provide verificationof the interaction through display 502.

Another device, which may optionally be coupled to controller 512, is acommunication device 506 for accessing remote resources 510 of adistributed system via network 508. Communication device 506 may includeany of a number of networking peripheral devices such as those used forcoupling to an Ethernet, Internet, or wide area network, and the like.Communication device 506 may further include a mechanism that providesconnectivity between controller 512 and the outside world. Note that anyor all of the components of system 500 illustrated in FIG. 5 andassociated hardware may be used in various embodiments of the presentdisclosure. The remote resources 510 may be part of a distributed systemand include any number of processors, memory, and other resources foroptimizing the structural parameters of the photonic device.

Controller 512 orchestrates operation of system 500 for optimizingstructural parameters of the photonic device. Processor 514 (e.g., oneor more central processing units, graphics processing units, and/ortensor processing units, etc.), memory 516 (e.g., volatile memory suchas DRAM and SRAM, non-volatile memory such as ROM, flash memory, and thelike), local storage 518 (e.g., magnetic memory such as computer diskdrives), and the photonic device simulator 522 are coupled to each otherthrough bus 520. Controller 512 includes software (e.g., instructionsincluded in memory 516 coupled to processor 514) and/or hardware logic(e.g., application specific integrated circuits, field-programmable gatearrays, and the like) that when executed by controller 512 causescontroller 512 or system 500 to perform operations. The operations maybe based on instructions stored within any one of, or a combination of,memory 516, local storage 518, physical device simulator 522, and remoteresources 510 accessed through network 508.

In the illustrated embodiment, the components of photonic devicesimulator 522 are utilized to optimize structural parameters of thephotonic device (e.g., MUX/DEMUX 114 of FIG. 1, demultiplexer 206 ofFIG. 2A, multiplexer 208 of FIG. 2B, demultiplexer 316 of FIG. 3A-D, andphotonic demultiplexer 400 of FIG. 4A-B). In some embodiments, system500 may optimize the structural parameters of the photonic device via,inter alia, simulations (e.g., operational and adjoint simulations) thatutilize a finite-difference time-domain (FDTD) method to model the fieldresponse (e.g., electric and magnetic fields within the photonicdevice). The operational simulation engine 526 provides instructions forperforming an electromagnetic simulation of the photonic deviceoperating in response to an excitation source within a simulatedenvironment. In particular, the operational simulation determines afield response of the simulated environment (and thus the photonicdevice, which is described by the simulated environment) in response tothe excitation source for determining a performance metric of thephysical device (e.g., based off an initial description or input designof the photonic device that describes the structural parameters of thephotonic device within the simulated environment with a plurality ofvoxels). The structural parameters may correspond, for example, to thespecific design, material compositions, dimensions, and the like of thephysical device. Fabrication loss calculation logic 528 providesinstructions for determining a fabrication loss, which is utilized toenforce a minimum feature size to ensure fabricability. In someembodiments, the fabrication loss is also used to enforce binarizationof the design (i.e., such that the photonic device includes a firstmaterial and a second material that are interspersed to form a pluralityof interfaces). Calculation logic 524 computes a loss metric determinedvia a loss function that incorporates a performance loss, based on theperformance metric, and the fabrication loss. Adjoint simulation engine530 is utilized in conjunction with the operational simulation engine526 to perform an adjoint simulation of the photonic device tobackpropagate the loss metric through the simulated environment via theloss function to determine how changes in the structural parameters ofthe photonic device influence the loss metric. Optimization engine 532is utilized to update the structural parameters of the photonic deviceto reduce the loss metric and generate a revised description (i.e.,revising the design) of the photonic device.

FIGS. 6A-6C respectively illustrate an initial set up of a simulatedenvironment describing a photonic device, performing an operationalsimulation of the photonic device in response to an excitation sourcewithin the simulated environment 608, and performing an adjointsimulation of the photonic device within the simulated environment 612.The initial set up of the simulated environment, 1-dimensionalrepresentation of the simulated environment, operational simulation ofthe physical device, and adjoint simulation of the physical device maybe implemented with system 500 illustrated in FIG. 5. As illustrated inFIG. 6A-C, simulated environment is represented in two-dimensions.However, it is appreciated that other dimensionality (e.g.,3-dimensional space) may also be used to describe simulated environmentand the photonic device. In some embodiments, optimization of structuralparameters of the photonic device illustrated in FIG. 6A-C may beachieved via an inverse design process including, inter alia,simulations (e.g., operational simulations and adjoint simulations) thatutilize a finite-difference time-domain (FDTD) method to model the fieldresponse (e.g., electric and magnetic field) to an excitation source.

FIG. 6A illustrates a demonstrative simulated environment 606 describinga photonic integrated circuit (i.e., a photonic device such as awaveguide, demultiplexer, and the like), in accordance with anembodiment of the present disclosure. More specifically, in response toreceiving an initial description of a photonic device defined by one ormore structural parameters (e.g., an input design), a system (e.g.,system 500 of FIG. 5) configures a simulated environment 606 to berepresentative of the photonic device. As illustrated, the simulatedenvironment 606 (and subsequently the photonic device) is described by aplurality of voxels 610, which represent individual elements (i.e.,discretized) of the two-dimensional (or other dimensionality) space.Each of the voxels is illustrated as two-dimensional squares; however,it is appreciated that the voxels may be represented as cubes or othershapes in three-dimensional space. It is appreciated that the specificshape and dimensionality of the plurality of voxels 610 may be adjusteddependent on the simulated environment 606 and photonic device beingsimulated. It is further noted that only a portion of the plurality ofvoxels 610 are illustrated to avoid obscuring other aspects of thesimulated environment 606.

Each of the plurality of voxels 610 may be associated with a structuralvalue, a field value, and a source value. Collectively, the structuralvalues of the simulated environment 606 describe the structuralparameters of the photonic device. In one embodiment, the structuralvalues may correspond to a relative permittivity, permeability, and/orrefractive index that collectively describe structural (i.e., material)boundaries or interfaces of the photonic device (e.g., interface pattern420 of FIG. 4B). For example, an interface 616 is representative ofwhere relative permittivity changes within the simulated environment 606and may define a boundary of the photonic device where a first materialmeets or otherwise interfaces with a second material. The field valuedescribes the field (or loss) response that is calculated (e.g., viaMaxwell's equations) in response to an excitation source described bythe source value. The field response, for example, may correspond to avector describing the electric and/or magnetic fields (e.g., in one ormore orthogonal directions) at a particular time step for each of theplurality of voxels 610. Thus, the field response may be based, at leastin part, on the structural parameters of the photonic device and theexcitation source.

In the illustrated embodiment, the photonic device corresponds to anoptical demultiplexer having a design region 614 (e.g., corresponding todispersive region 332 of FIG. 3A, and/or dispersive region 406 of FIG.4A), in which structural parameters of the physical device may beupdated or otherwise revised. More specifically, through an inversedesign process, iterative gradient-based optimization of a loss metricdetermined from a loss function is performed to generate a design of thephotonic device that functionally causes a multi-channel optical signalto be demultiplexed and guided from input port 602 to a correspondingone of the output ports 604. Thus, input port 602 (e.g., correspondingto input region 302 of FIG. 3A, input region 402 of FIG. 4A, and thelike) of the photonic device corresponds to a location of an excitationsource to provide an output (e.g., a Gaussian pulse, a wave, a waveguidemode response, and the like). The output of the excitation sourceinteracts with the photonic device based on the structural parameters(e.g., an electromagnetic wave corresponding to the excitation sourcemay be perturbed, retransmitted, attenuated, refracted, reflected,diffracted, scattered, absorbed, dispersed, amplified, or otherwise asthe wave propagates through the photonic device within simulatedenvironment 606). In other words, the excitation source may cause thefield response of the photonic device to change, which is dependent onthe underlying physics governing the physical domain and the structuralparameters of the photonic device. The excitation source originates oris otherwise proximate to input port 602 and is positioned to propagate(or otherwise influence the field values of the plurality of voxels)through the design region 614 towards output ports 604 of the photonicdevice. In the illustrated embodiment, the input port 602 and outputports 604 are positioned outside of the design region 614. In otherwords, in the illustrated embodiment, only a portion of the structuralparameters of the photonic device is optimizable.

However, in other embodiments, the entirety of the photonic device maybe placed within the design region 614 such that the structuralparameters may represent any portion or the entirety of the design ofthe photonic device. The electric and magnetic fields within thesimulated environment 606 (and subsequently the photonic device) maychange (e.g., represented by field values of the individual voxels thatcollectively correspond to the field response of the simulatedenvironment) in response to the excitation source. The output ports 604of the optical demultiplexer may be used for determining a performancemetric of the photonic device in response to the excitation source(e.g., power transmission from input port 602 to a specific one of theoutput ports 604). The initial description of the photonic device,including initial structural parameters, excitation source, performanceparameters or metrics, and other parameters describing the photonicdevice, are received by the system (e.g., system 500 of FIG. 5) and usedto configure the simulated environment 606 for performing afirst-principles based simulation of the photonic device. These specificvalues and parameters may be defined directly by a user (e.g., of system500 in FIG. 5), indirectly (e.g., via controller 512 cullingpre-determined values stored in memory 516, local storage 518, or remoteresources 510), or a combination thereof.

FIG. 6B illustrates an operational simulation of the photonic device inresponse to an excitation source within simulated environment 608, inaccordance with various aspects of the present disclosure. In theillustrated embodiment, the photonic device is an optical demultiplexerstructured to optically separate each of a plurality of distinctwavelength channels included in a multi-channel optical signal receivedat input port 602 and respectively guide each of the plurality ofdistinct wavelength channels to a corresponding one of the plurality ofoutput ports 604. The excitation source may be selected (randomly orotherwise) from the plurality of distinct wavelength channels andoriginates at input port 602 having a specified spatial, phase, and/ortemporal profile. The operational simulation occurs over a plurality oftime steps, including the illustrated time step. When performing theoperational simulation, changes to the field response (e.g., the fieldvalue) for each of the plurality of voxels 610 are incrementally updatedin response to the excitation source over the plurality of time steps.The changes in the field response at a particular time step are based,at least in part, on the structural parameters, the excitation source,and the field response of the simulated environment 608 at theimmediately prior time step included in the plurality of time steps.Similarly, in some embodiments the source value of the plurality ofvoxels 610 is updated (e.g., based on the spatial profile and/ortemporal profile describing the excitation source). It is appreciatedthat the operational simulation is incremental and that the field values(and source values) of the simulated environment 608 are updatedincrementally at each time step as time moves forward for each of theplurality of time steps during the operational simulation. It is furthernoted that in some embodiments, the update is an iterative process andthat the update of each field and source value is based, at least inpart, on the previous update of each field and source value.

Once the operational simulation reaches a steady state (e.g., changes tothe field values in response to the excitation source substantiallystabilize or reduce to negligible values) or otherwise concludes, one ormore performance metrics may be determined. In one embodiment, theperformance metric corresponds to the power transmission at acorresponding one of the output ports 604 mapped to the distinctwavelength channel being simulated by the excitation source. In otherwords, in some embodiments, the performance metric represents power (atone or more frequencies of interest) in the target mode shape at thespecific locations of the output ports 604. A loss value or metric ofthe input design (e.g., the initial design and/or any refined design inwhich the structural parameters have been updated) based, at least inpart, on the performance metric may be determined via a loss function.The loss metric, in conjunction with an adjoint simulation, may beutilized to determine a structural gradient (e.g., influence ofstructural parameters on loss metric) for updating or otherwise revisingthe structural parameters to reduce the loss metric (i.e. increase theperformance metric). It is noted that the loss metric is further basedon a fabrication loss value that is utilized to enforce a minimumfeature size of the photonic device to promote fabricability of thedevice.

FIG. 6C illustrates an example adjoint simulation within simulatedenvironment 612 by backpropagating a loss metric, in accordance withvarious aspects of the present disclosure. More specifically, theadjoint simulation is a time-backwards simulation in which a loss metricis treated as an excitation source that interacts with the photonicdevice and causes a loss response. In other words, an adjoint (orvirtual source) based on the loss metric is placed at the output region(e.g., output ports 604) or other location that corresponds to alocation used when determining the performance metric. The adjointsource(s) is then treated as a physical stimuli or an excitation sourceduring the adjoint simulation. A loss response of the simulatedenvironment 612 is computed for each of the plurality of time steps(e.g., backwards in time) in response to the adjoint source. The lossresponse collectively refers to loss values of the plurality of voxelsthat are incrementally updated in response to the adjoint source overthe plurality of time steps. The change in loss response based on theloss metric may correspond to a loss gradient, which is indicative ofhow changes in the field response of the physical device influence theloss metric. The loss gradient and the field gradient may be combined inthe appropriate way to determine a structural gradient of the photonicdevice/simulated environment (e.g., how changes in the structuralparameters of the photonic device within the simulated environmentinfluence the loss metric). Once the structural gradient of a particularcycle (e.g., operational and adjoint simulation) is known, thestructural parameters may be updated to reduce the loss metric andgenerate a revised description or design of the photonic device.

In some embodiments, iterative cycles of performing the operationalsimulation, and adjoint simulation, determining the structural gradient,and updating the structural parameters to reduce the loss metric areperformed successively as part of an inverse design process thatutilizes iterative gradient-based optimization. An optimization schemesuch as gradient descent may be utilized to determine specific amountsor degrees of changes to the structural parameters of the photonicdevice to incrementally reduce the loss metric. More specifically, aftereach cycle the structural parameters are updated (e.g., optimized) toreduce the loss metric. The operational simulation, adjoint simulation,and updating the structural parameters are iteratively repeated untilthe loss metric substantially converges or is otherwise below or withina threshold value or range such that the photonic device provides thedesired performed while maintaining fabricability.

One problem in designing physical devices such as the photonic devicesdescribed above is that, even if a simulated photonic device is designedthat is highly performant, physical realities of manufacturing thedesigned photonic device may reduce the actual performance of thephotonic device as manufactured. For example, differences in operatingconditions for a fabrication system, including but not limited to anambient temperature, erosion, dilation, waveguide thickness, structureout of plane, sidewall angle, a surface roughness of a material to beprocessed, other material imperfections of a material to be processed,misalignment of the fabrication system, and optical aberrations withinthe fabrication system, may cause differences to be introduced betweenthe structure of the physical device as designed and the structure ofthe physical device as manufactured. That is, the different operatingconditions may cause the features of the physical device to be smaller,larger, or differently shaped than the design that is provided to thefabrication system. What is desired are design techniques that willresult in designs for physical devices that are highly performant andare also robust to changes in operating conditions of the fabricationsystem.

FIG. 7A is a flow chart 700 illustrating example time steps for anoperational simulation 702 and an adjoint simulation 704, in accordancewith various aspects of the present disclosure. Flow chart 700 is onepossible implementation that a system (e.g., system 500 of FIG. 5) mayuse to perform the operational simulation 702 and adjoint simulation 704of the simulated environment (e.g., simulated environment of FIG. 6A-C)describing a photonic integrated circuit (e.g., an optical deviceoperating in an electromagnetic domain such a photonic demultiplexer).In the illustrated embodiment, the operational simulation 702 utilizes afinite-difference time-domain (FDTD) method to model the field response(both electric and magnetic) or loss response at each of a plurality ofvoxels (e.g., plurality of voxels 610 illustrated in FIG. 6A-C) for aplurality of time steps in response to physical stimuli corresponding toan excitation source and/or adjoint source.

As illustrated in FIG. 7A, the operational simulation 702 includes aconfiguration portion 748 and a simulation portion 750. In theconfiguration portion 748, an initial design 736 is received thatincludes structural parameters for a physical device such as a photonicdevice to be simulated. The structural parameters may represent theexact intended design for the physical device, or may represent a designfor the physical device as would be fabricated under a nominal ordefault set of operating conditions. In some embodiments, the initialdesign 736 may include the structural parameters and an indication ofthe assumed operating conditions under which the structural parameterswould have been fabricated. In some embodiments, the initial design 736may include ranges of operating conditions under which the structuralparameters should be analyzed by the remainder of the operationalsimulation 702.

After receiving the initial design 736, the operational simulation 702generates a plurality of perturbed structural parameters 706. Eachperturbed structural parameter 706 represents the structural parametersof the initial design 736 as they would be fabricated by the fabricationsystem under a different set of operating conditions. A fabricationmodel may be used to simulate the fabrication of the photonic devicebased on the initial structural parameters and the operating conditionsin order to generate the perturbed structural parameters 706. Forexample, the temperature of the device might be different from thenominal temperature, resulting in a change in the refractive index orother material properties of the device. As another example, there maybe structural parameters that are perturbed including but not limited toan extra rounding of corners.

In some embodiments, ranges of values for each of the operatingconditions may be predetermined. Any suitable technique may then be usedto determine the sets of operating conditions for generating theperturbed structural parameters 706. For example, values within thepredetermined ranges of values may be stochastically sampled for each ofthe operating conditions, and combinations of the stochastically sampledvalues may be used as the sets of operating conditions. Alternatively,extremal values of the operating conditions may be used (this is thesimplest case of uniform sampling). As another example, values withinthe predetermined ranges of values may be uniformly sampled for eachoperating condition, and combinations of the uniformly sampled valuesmay be used as the sets of operating conditions. As yet another example,a sensitivity for each operating condition may be determined, and thenvalues within the predetermined ranges of values may be sampled in anon-linear manner based on the determined sensitivities. Thesensitivities may be determined by analyzing the results obtained with aplurality of sets of operating conditions that vary each operatingcondition separately.

After the perturbed structural parameters 706 are determined, theoperational simulation 702 proceeds to a simulation portion 750, whichis performed separately for each of the perturbed structural parameters706. The simulation portion 750 occurs over a plurality of time-steps(e.g., from an initial time step to a final time step over apre-determined or conditional number of time steps having a specifiedtime step size) and models changes (e.g., from the initial field values712) in electric and magnetic fields of a plurality of voxels describingthe simulated environment and/or photonic device that collectivelycorrespond to the field response. More specifically, update operations(e.g., update operation 714, update operation 716, and update operation718) are iterative and based on the field response, structuralparameters 708 (that is, for a selected one of the perturbed structuralparameters 706), and one or more excitation sources 710. Each updateoperation is succeeded by another update operation, which arerepresentative of successive steps forward in time within the pluralityof time steps. For example, update operation 716 updates the fieldvalues 740 (see, e.g., FIG. 7B) based on the field response determinedfrom the previous update operation 714, excitation sources 710, and thestructural parameters 708. Similarly, update operation 718 updates thefield values 742 (see, e.g., FIG. 7B) based on the field responsedetermined from update operation 716. In other words, at each time stepof the operational simulation the field values (and thus field response)are updated based on the previous field response and structuralparameters of the photonic device.

Once the final time step of the simulation portion 750 is performed, aperformance loss function 720 is used to determine a performance lossvalue 722 associated with the selected perturbed structural parameter706. The performance loss values 722 for each of the perturbedstructural parameters 706 are then combined into a total performanceloss value that can be used to determine (or used as) a loss metric 724.The performance loss values 722 may be combined using any suitabletechnique. For example, in some embodiments, a linear combination of theperformance loss values 722 may be used as the total performance lossvalue. Another example is that the performance loss of only the poorestperforming device may be used. As yet another example, in embodimentswherein a non-linear sampling of the operating conditions was performedbased on sensitivities associated with each operating condition, anon-linear combination of the performance loss values 722 based on thesensitivities may be performed to create the total performance lossvalue.

From the loss metric 724, loss gradients may be determined at block 726.The loss gradients determined from block 726 may be treated as adjointor virtual sources (e.g., physical stimuli or excitation sourceoriginating at an output region or port) which are backpropagated inreverse (from the final time step incrementally through the plurality oftime steps until reaching the initial time step via update operation728, update operation 730, and update operation 732) to determinestructural gradient 734. Because it is determined based on the totalperformance loss value, the structural gradient 734 is associated withthe initial design 736, as opposed to an individual perturbed structuralparameter 706. This allows the initial design 736 to be updated insteadof having to individually process each of the perturbed structuralparameters 706 and propagate changes in the design back to the initialdesign 736, thus eliminating a large amount of unnecessary computation.

In the illustrated embodiment, the FDTD solve (e.g., simulation portion750 of the operational simulation 702) and backward solve (e.g., adjointsimulation 704) problem are described pictorially, from a high-level,using only “update” and “loss” operations as well as their correspondinggradient operations. The simulation is set up initially in which thestructural parameters, physical stimuli (i.e., excitation source), andinitial field states of the simulated environment (and photonic device)are provided (e.g., via an initial description and/or input design). Asdiscussed previously, the field values are updated in response to theexcitation source based on the structural parameters. More specifically,the update operation is given by ϕ, where

=ϕ(

,

,

) for

=1, . . . ,

. Here,

corresponds to the total number of time steps (e.g., the plurality oftime steps) for the operational simulation, where

corresponds to the field response (the field value associated with theelectric and magnetic fields of each of the plurality of voxels) of thesimulated environment at time step

,

, corresponds to the excitation source(s) (the source value associatedwith the electric and magnetic fields for each of the plurality ofvoxels) of the simulated environment at time step

, and

corresponds to the structural parameters describing the topology and/ormaterial properties of the physical device (e.g., relative permittivity,index of refraction, and the like).

It is noted that using the FDTD method, the update operation mayspecifically be stated as:

ϕ(

,

,

)=A(

)

+B(

)

.  (1)

That is to say the FDTD update is linear with respect to the field andsource terms. Concretely, A(

) ∈

^(N×N) and B(

) ∈

^(N×N) are linear operators which depend on the structure parameters,

, and act on the fields,

, and the sources,

, respectively. Here, it is assumed that

,

∈

^(N) where N is the number of FDTD field components in the operationalsimulation. Additionally, the loss operation (e.g., loss function) maybe given by L=ƒ

, . . . ,

), which takes as input the computed fields and produces a single,real-valued scalar (e.g., the loss metric) that can be reduced and/orminimized.

In terms of revising or otherwise optimizing the structural parametersof the physical device, the relevant quantity to produce is

$\frac{dL}{dz},$

which is used to describe the influence of changes in the structuralparameters of the initial design 736 on the loss value and is denoted asthe structural gradient 734 illustrated in FIG. 7A.

FIG. 7B is a chart 738 illustrating the relationship between the updateoperation for the operational simulation and the adjoint simulation(e.g., backpropagation), in accordance with an embodiment of the presentdisclosure. More specifically, FIG. 7B summarizes the operational andadjoint simulation relationships that are involved in computing thestructural gradient,

$\frac{dL}{dz},$

which include

$\frac{\partial L}{\partial x_{i}},\frac{\partial x_{i + 1}}{\partial x_{i}},\frac{dL}{dx_{i}},{{and}\mspace{14mu}{\frac{\partial x_{i}}{\partial z}.}}$

The update operation 716 of the operational simulation 702 updates thefield values 740,

, of the plurality of voxels at the

th time step to the next time step (i.e.,

+1 time step), which correspond to the field values 742,

. The gradients 744 are utilized to determine for the backpropagation(e.g., update operation 730 backwards in time), which combined with thegradients 746 are used, at least in part, to calculate the structuralgradient,

$\frac{dL}{d_{d}}.\frac{\partial L}{\partial x_{i}}$

is the contribution of each field to the loss metric, L. It is notedthat this is the partial derivative, and therefore does not take intoaccount the causal relationship of

→

. Thus,

$\frac{\partial x_{i + 1}}{\partial x_{i}}$

is utilized which encompasses the

→

relationship. The loss gradient,

$\frac{dL}{dx_{i}}$

may also be used to compute the structural gradient,

$\frac{dL}{dz},$

and corresponds to the total derivative of the field with respect toloss value, L. The loss gradient,

$\frac{dL}{dx_{i}},$

at a particular time step,

, is equal to the summation of

$\frac{\partial L}{\partial x_{i}} + {\frac{dL}{dx_{i + 1}}{\frac{\partial x_{i + 1}}{\partial x_{i}}.}}$

Finally,

$\frac{\partial x_{i}}{\partial z},$

which corresponds to the field gradient, is used which is thecontribution to

$\frac{dL}{dz}$

from each time/update step.

In particular, the memory footprint to directly compute

∂ L ⁢ ⁢ and ⁢ ⁢ d ⁢ L d ⁢ z

is so large that it is difficult to store more than a handful of stateTensors. The state Tensor corresponds to storing the values of all ofthe FDTD cells (e.g., the plurality of voxels) for a single simulationtime step. It is appreciated that the term “tensor” may refer to tensorsin a mathematical sense or as described by the TensorFlow frameworkdeveloped by Alphabet, Inc. In some embodiments the term “tensor” refersto a mathematical tensor which corresponds to a multidimensional arraythat follows specific transformation laws. However, in most embodiments,the term “tensor” refers to TensorFlow tensors, in which a tensor isdescribed as a generalization of vectors and matrices to potentiallyhigher dimensions (e.g., n-dimensional arrays of base data types), andis not necessarily limited to specific transformation laws. For example,for the general loss function ƒ, it may be necessary to store thefields,

, for all time steps,

. This is because, for most choices of ƒ, the gradient will be afunction of the arguments of ƒ. This difficulty is compounded by thefact that the values of for larger values of

are needed before the values for smaller

due to the incremental updates of the field response and/or throughbackpropagation of the loss metric, which may prevent the use of schemesthat attempt to store only the values

∂ L ,

at an immediate time step.

An additional difficulty is further illustrated when computing thestructural gradient,

$\frac{dL}{dz},$

which is given by:

dL dz = ∑ i ⁢ ∂ L dx i ⁢ ∂ z . ( 2 )

For completeness, the full form of the first term in the sum,

$\frac{dL}{dz},$

is expressed as:

$\begin{matrix}{\frac{dL}{{dx}_{i}} = {\frac{\partial L}{\partial x_{i}} + {\frac{dL}{{dx}_{i + 1}}{\frac{\partial x_{i + 1}}{\partial x_{i}}.}}}} & (3)\end{matrix}$

Based on the definition of ϕ as described by equation (1), it is notedthat

${\frac{\partial x_{i + 1}}{\partial x_{i}} = {A(z)}},$

which can be substituted in equation (3) to arrive at an adjoint updatefor backpropagation (e.g., the update operations such as updateoperation 730), which can be expressed as:

$\begin{matrix}{{\frac{dL}{{dx}_{i}} = {\frac{\partial L}{\partial x_{i}} + {\frac{dL}{{dx}_{i + 1}}{A(z)}}}},} & (4) \\{and} & \; \\{{\nabla_{x_{i}}L} = {{{A(z)}^{T}{\nabla_{x_{i + 1}}L}} + {\frac{\partial L^{T}}{\partial x_{i}}.}}} & (5)\end{matrix}$

The adjoint update is the backpropagation of the loss gradient (e.g.,from the loss metric) from later to earlier time steps and may bereferred to as a backwards solve for

$\frac{dL}{{dx}_{i}}.$

More specifically, the loss gradient may initially be based upon thebackpropagation of a loss metric determined from the operationalsimulation with the loss function. The second term in the sum of thestructural gradient,

$\frac{dL}{dz},$

corresponds to the field gradient and is denoted as:

∂ z = d ⁢ ϕ ⁡ ( x i - 1 , i - 1 , z ) dz = dA ⁡ ( z ) dz ⁢ x i - 1 + dB ⁡ ( z) dz ⁢ i - 1 , ( 6 )

for the particular form of ϕ described by equation (1). Thus, each termof the sum associated

$\frac{dL}{dz}$

depends on both

d ⁢ L

for

>=

and

for

<

. Since the dependency chains of these two terms are in oppositedirections, it is concluded that computing

$\frac{dL}{dz}$

in this way requires the storage of

values for all of

. In some embodiments, the need to store all field values may bemitigated by a reduced representation of the fields.

FIG. 8 is a flowchart that illustrates a non-limiting example embodimentof a method 800 for generating a design of physical device such as aphotonic integrated circuit, in accordance with various aspects of thepresent disclosure. It is appreciated that method 800 is an inversedesign process that may be accomplished by performing operations with asystem (e.g., system 500 of FIG. 5) to perform iterative gradient-basedoptimization of a loss metric determined from a loss function thatincludes at least a performance loss and a fabrication loss. In the sameor other embodiments, method 800 may be included as instructionsprovided by at least one machine-accessible storage medium (e.g.,non-transitory memory) that, when executed by a machine, will cause themachine to perform operations for generating and/or improving the designof the photonic integrated circuit. It is further appreciated that theorder in which some or all of the process blocks appear in method 800should not be deemed limiting. Rather, one of ordinary skill in the arthaving the benefit of the present disclosure will understand that someof the process blocks may be executed in a variety of orders notillustrated, or even in parallel.

From a start block, the method 800 proceeds to block 802, where aninitial design 736 of a physical device such as a photonic integratedcircuit is received. In some embodiments, the physical device may beexpected to have a certain functionality (e.g., perform as an opticaldemultiplexer) after optimization. The initial design 736 may describestructural parameters of the physical device within a simulatedenvironment. The simulated environment may include a plurality of voxelsthat collectively describe the structural parameters of the physicaldevice. Each of the plurality of voxels is associated with a structuralvalue to describe the structural parameters, a field value to describethe field response (e.g., the electric and magnetic fields in one ormore orthogonal directions) to physical stimuli (e.g., one or moreexcitation sources), and a source value to describe the physicalstimuli. In some embodiments the initial design 736 may be a firstdescription of the physical device in which values for the structuralparameters may be random values or null values outside of input andoutput regions such that there is no bias for the initial (e.g., first)design. It is appreciated that the initial description or input designmay be a relative term. Thus, in some embodiments an initial descriptionmay be a first description of the physical device described within thecontext of the simulated environment (e.g., a first input design forperforming a first operational simulation).

However, in other embodiments, the term initial description may refer toan initial description of a particular cycle (e.g., of performing anoperational simulation 702, operating an adjoint simulation 704, andupdating the structural parameters). In such an embodiment, the initialdesign 736 or design of that particular cycle may correspond to arevised description or refined design (e.g., generated from a previouscycle). In some embodiments, the simulated environment includes a designregion that includes a portion of the plurality of voxels which havestructural parameters that may be updated, revised, or otherwise changedto optimize the structural parameters of the physical device. In thesame or other embodiments, the structural parameters are associated withgeometric boundaries and/or material compositions of the physical devicebased on the material properties (e.g., relative permittivity, index ofrefraction, etc.) of the simulated environment.

At block 804, perturbed structural parameters 706 are generated based onthe initial design 736. As discussed above, sets of operating conditionsmay be generated within the ranges of valid operating conditions usingany suitable technique, including but not limited to stochasticsampling, linear sampling, and non-linear sampling based onsensitivities. The sets of operating conditions may then be used tosimulate fabrication based on initial structural parameters within theinitial design 736 in order to generate the perturbed structuralparameters 706.

The method 800 then proceeds to a for-loop defined between a for-loopstart block 806 and a for-loop end block 814, wherein each of theperturbed structural parameters 706 is processed. From the for-loopstart block 806, the method 800 proceeds to block 808, where a simulatedenvironment is configured to be representative of the perturbedstructural parameters of a physical device (e.g., photonic device). Oncethe perturbed structural parameters have been received or otherwiseobtained, the simulated environment is configured (e.g., the number ofvoxels, shape/arrangement of voxels, and specific values for thestructural value, field value, and/or source value of the voxels are setbased on the perturbed structural parameters).

In some embodiments the simulated environment includes a design regionoptically coupled between a first communication region and a pluralityof second communication regions. In some embodiments, the firstcommunication region may correspond to an input region or port (e.g.,where an excitation source originates), while the second communicationmay correspond to a plurality of output regions or ports (e.g., whendesigning an optical demultiplexer that optically separates a pluralityof distinct wavelength channels included in a multi-channel opticalsignal received at the input port and respectively guiding each of thedistinct wavelength channels to a corresponding one of the plurality ofoutput ports). However, in other embodiments, the first communicationregion may correspond to an output region or port, while the pluralityof second communication regions corresponds to a plurality of inputports or region (e.g., when designing an optical multiplexer thatoptically combines a plurality of distinct wavelength signals receivedat respective ones of the plurality of input ports to form amulti-channel optical signal that is guided to the output port).

Block 810 shows mapping each of a plurality of distinct wavelengthchannels to a respective one of the plurality of second communicationregions. The distinct wavelength channels may be mapped to the secondcommunication regions by virtue of the initial design 736 of thephysical device. For example, a loss function may be chosen thatassociates a performance metric of the physical device with powertransmission from the input port to individual output ports for mappedchannels. In one embodiment, a first channel included in the pluralityof distinct wavelength channels is mapped to a first output port,meaning that the performance metric of the physical device for the firstchannel is tied to the first output port. Similarly, other output portsmay be mapped to the same or different channels included in theplurality of distinct wavelength channels such that each of the distinctwavelength channels is mapped to a respective one of the plurality ofoutput ports (i.e., second communication regions) within the simulatedenvironment. In one embodiment, the plurality of second communicationregions includes four regions and the plurality of distinct wavelengthchannels includes four channels that are each mapped to a correspondingone of the four regions. In other embodiments, there may be a differentnumber of the second communication regions (e.g., 8 regions) and adifferent number of channels (e.g., 8 channels) that are each mapped toa respective one of the second communication regions.

Block 812 illustrates performing an operational simulation of thephysical device within the simulated environment operating in responseto one or more excitation sources to determine a performance loss value.More specifically, in some embodiments an electromagnetic simulation isperformed in which a field response of the photonic integrated circuitis updated incrementally over a plurality of time steps to determine howthe how the field response of the physical device changes due to theexcitation source. The field values of the plurality of voxels areupdated in response to the excitation source and based, at least inpart, on the structural parameters of the integrated photonic circuit.Additionally, each update operation at a particular time step may alsobe based, at least in part, on a previous (e.g., immediately prior) timestep.

Consequently, the operational simulation simulates an interactionbetween the photonic device (i.e., the photonic integrated circuit) anda physical stimuli (i.e., one or more excitation sources) to determine asimulated output of the photonic device (e.g., at one or more of theoutput ports or regions) in response to the physical stimuli. Theinteraction may correspond to any one of, or combination of aperturbation, retransmission, attenuation, dispersion, refraction,reflection, diffraction, absorption, scattering, amplification, orotherwise of the physical stimuli within electromagnetic domain due, atleast in part, to the structural parameters of the photonic device andunderlying physics governing operation of the photonic device. Thus, theoperational simulation simulates how the field response of the simulatedenvironment changes due to the excitation source over a plurality oftime steps (e.g., from an initial to final time step with apre-determined step size).

In some embodiments, the simulated output may be utilized to determineone or more performance metrics of the physical device. For example, theexcitation source may correspond to a selected one of a plurality ofdistinct wavelength channels that are each mapped to one of theplurality of output ports. The excitation source may originate at or bedisposed proximate to the first communication region (i.e., input port)when performing the operational simulation. During the operationalsimulation, the field response at the output port mapped to the selectedone of the plurality of distinct wavelength channels may then beutilized to determine a simulated power transmission of the photonicintegrated circuit for the selected distinct wavelength channel. Inother words, the operational simulation may be utilized to determine theperformance metric that includes determining a simulated powertransmission of the excitation source from the first communicationregion, through the design region, and to a respective one of theplurality of second communication regions mapped to the selected one ofthe plurality of distinct wavelength channels. In some embodiments, theexcitation source may cover the spectrum of all of the plurality ofoutput ports (e.g., the excitation source spans at least the targetedfrequency ranges for the bandpass regions for each of the plurality ofdistinct wavelength channels as well as the corresponding transitionband regions, and at least portions of the corresponding stopbandregions) to determine a performance metric (i.e., simulated powertransmission) associated with each of the distinct wavelength channelsfor the photonic integrated circuit. In some embodiments, one or morefrequencies that span the passband of a given one of the plurality ofdistinct wavelength channels is selected randomly to optimize the design(e.g., batch gradient descent while having a full width of each passbandincluding ripple in the passband that meets the target specifications).In the same or other embodiments, each of the plurality of distinctwavelength channels has a common bandwidth with different centerwavelengths. The performance metric may then be used to generate aperformance loss value for the set of perturbed structural parameters706. The performance loss value may correspond to a difference betweenthe performance metric and a target performance metric of the physicaldevice.

The method 800 then proceeds to the for-loop end block 814. If furtherperturbed structural parameters 706 remain to be processed, then themethod 800 returns to for-loop start block 806 to process the next setof perturbed structural parameters 706. Otherwise, if performance lossvalues have been obtained for all of the perturbed structural parameters706, then the method advances to block 816.

At block 816, the performance loss values 722 are combined to generate acombined performance loss value. As discussed above, any suitabletechnique may be used to combine the separate performance loss values,including but not limited to linear combination and non-linearcombination based on sensitivities for each operating condition.

Block 818 shows determining a loss metric based on the combinedperformance loss value and a fabrication loss associated with a minimumfeature size. In some embodiments the loss metric is determined via aloss function that includes both the performance loss value and thefabrication loss as input values. In some embodiments, a minimum featuresize for the design region of the simulated environment may be providedto promote fabricability of the design generated by the inverse designprocess. The fabrication loss is based, at least in part, on the minimumfeature size and the perturbed structural parameters of the designregion. More specifically, the fabrication loss enforces the minimumfeature size for the design such that the design region does not havestructural elements with a diameter less than the minimum feature size.This helps this system provide designs that meet certain fabricabilityand/or yield requirements. In some embodiments the fabrication loss alsohelps enforce binarization of the design (i.e., rather than mixing thefirst and second materials together to form a third material, the designincludes regions of the first material and the second material that areinhomogeneously interspersed).

In some embodiments the fabrication loss is determined by generating aconvolution kernel (e.g., circular, square, octagonal, or otherwise)with a width equal to the minimum feature size. The convolution kernelis then shifted through the design region of the simulated environmentto determine voxel locations (i.e., individual voxels) within the designregion that fit the convolution kernel within the design region withoutextending beyond the design region. The convolution kernel is thenconvolved at each of the voxel locations with the structural parametersassociated with the voxel locations to determine first fabricationvalues. The structural parameters are then inverted and the convolutionkernel is convolved again at each of the voxel locations with theinverted structural parameters to determine second fabrication values.The first and second fabrication values are subsequently combined todetermine the fabrication loss for the design region. This process ofdetermining the fabrication loss may promote structural elements of thedesign region having a radius of curvature less having a magnitude ofless than a threshold size (i.e., inverse of half the minimum featuresize).

Block 820 illustrates backpropagating the loss metric via the lossfunction through the simulated environment to determine an influence ofchanges in the structural parameters on the loss metric (i.e.,structural gradient). The loss metric is treated as an adjoint orvirtual source and is backpropagated incrementally from a final timestep to earlier time steps in a backwards simulation to determine thestructural gradient of the physical device.

Block 822 shows revising a design of the physical device (e.g.,generated a revised description) by updating the structural parametersof the initial design 736 to adjust the loss metric. In someembodiments, adjusting for the loss metric may reduce the loss metric.However, in other embodiments, the loss metric may be adjusted orotherwise compensated in a manner that does not necessarily reduce theloss metric, In one embodiment, adjusting the loss metric may maintainfabricability while providing a general direction within theparameterization space to obtain designs that will ultimately result inincreased performance while also maintaining device fabricability andtargeted performance metrics. In some embodiments, the reviseddescription is generated by utilizing an optimization scheme after acycle of operational and adjoint simulations via a gradient descentalgorithm, Markov Chain Monte Carlo algorithm, or other optimizationtechniques. Put in another way, iterative cycles of simulating thephysical device, determining a loss metric, backpropagating the lossmetric, and updating the structural parameters to adjust the loss metricmay be successively performed until the loss metric substantiallyconverges such that the difference between the performance metric andthe target performance metric is within a threshold range while alsoaccounting for fabricability and binarization due to the fabricationloss. By using multiple perturbed structural parameters to determine theperformance loss value, the update of the initial design 736 will alsoaccount for robustness to differing operating conditions duringfabrication. In some embodiments, the term “converges” may simplyindicate the difference is within the threshold range and/or below somethreshold value.

At decision block 824, a determination is made regarding whether theloss metric substantially converges such that the difference between theperformance metric and the target performance metric is within athreshold range. Iterative cycles of simulating the physical device withthe excitation source selected from the plurality of distinct wavelengthchannels, backpropagating the loss metric, and revising the design byupdating the structural parameters to reduce the loss metric until theloss metric substantially converges such that the difference between theperformance metric and the target performance metric is within athreshold range. In some embodiments, the structural parameters of thedesign region of the integrated photonic circuit are revised whenperforming the cycles to cause the design region of the photonicintegrated circuit to optically separate each of the plurality ofdistinct wavelength channels from a multi-channel optical signalreceived via the first communication region and guide each of theplurality of distinct wavelength channels to the corresponding one ofthe plurality of second communication regions.

If the determination is that the loss metric has not converged, then theresult of decision block 824 is NO, and the method 800 returns to block804 to iterate on the revised initial design 736. Otherwise, if thedetermination is that the loss metric has converged, then the result ofdecision block 824 is YES and the method 800 advances to block 826.

Block 826 illustrates outputting an optimized design of the physicaldevice in which the structural parameters have been updated to have thedifference between the performance metric and the target performancemetric within a threshold range while also enforcing a minimum featuresize and binarization. The method 800 then proceeds to an end block andterminates.

While computing perturbed structural parameters based on an initialdesign and then processing each set of perturbed structural parametersto generate a combined performance loss value can help ensure robustnessto differing operating conditions during manufacturing, it is not theonly technique that may be used. FIG. 9 is a flow chart 900 illustratingexample time steps for an operational simulation 902 and an adjointsimulation 904, in accordance with various aspects of the presentdisclosure. In the flow chart 900, instead of generating perturbedstructural parameters and then simulating the performance of each set ofperturbed structural parameters as illustrated in FIG. 7A and FIG. 8,only the structural parameters of an initial design 936 (which includessimilar information as the initial design 736 discussed above) aresimulated. Most of the features illustrated in flow chart 900 (e.g.,excitation sources 910, initial field values 912, update operation 914,the entire adjoint simulation 904, etc.), are similar to the actionsillustrated in FIG. 7A, and so are not described in detail for the sakeof brevity.

As shown, the structural parameters 908 of the initial design 936 areprocessed along with excitation sources 910 and initial field values 912in an operational simulation 902. The operational simulation 902includes update steps, such as update operation 914, update operation916, and update operation 918, in which the field values are updatedbased on the excitation sources 910 and the result of previous updateoperations (as was discussed above with respect to update operation 714,update operation 716, and update operation 718 of FIG. 7A). Also, aswith FIG. 7A, in some embodiments more than the three illustrated updateoperations may be performed, though only three update operations areillustrated herein for the sake of brevity. The field values generatedby update operation 914, update operation 916, and update operation 918are provided to a performance loss function 920.

In addition to this simulation of performance, the structural parameters(and, optionally, other aspects of the initial design 936) are alsoprovided to a fabrication model 938. The fabrication model 938 istrained to determine how perturbations of the operating conditions willaffect the structural parameters, and the output of the fabricationmodel 938 is provided to a perturbation model 940. The perturbationmodel 940 also receives the field values from each of the updateoperations, and uses the output of the fabrication model 938 and thefield values to provide a robustness loss function 942 that reflects howrobust the initial design 936 is to changes in the operating conditions.The perturbation model 940 may use the field values because it ispossible that operating conditions may cause changes in structuralparameters that, based on the field values at the changed location, canbe determined to have little to no effect on the performance of thephysical device. For example, the fabrication model 938 may determinethat successful reproduction of a particular feature is likely to behighly dependent on the operating conditions, while the perturbationmodel 940 learns from the field values that the field values are zero atthe location of the particular feature. In such a situation, therobustness loss would be minimal for the particular feature, becausesuccessful reproduction of the particular feature would not have asignificant effect on performance of the physical device.

As shown, the performance loss function 920 and the robustness lossfunction 942 are then combined to create a loss metric 924, for whichgradients are determined at block 926, and a set of update operations(update operation 928, update operation 930, update operation 932) areperformed to generate a structural gradient 934. The performance lossfunction 920 and the robustness loss function 942 may be combined in anysuitable manner, including but not limited to a linear combination oraddition of the respective values. The adjoint simulation 904 is similarto the adjoint simulation 704 illustrated in FIG. 7A, and so is notdescribed here in detail for the sake of brevity. Likewise, therelationship between the operational simulation 902 and the adjointsimulation 904 is similar to the relationship between the operationalsimulation 702 and the adjoint simulation 704 as illustrated in FIG. 7B,and so further description of the relationship between operationalsimulation 902 and adjoint simulation 904 is also not provided for thesake of brevity.

FIG. 10 is a flowchart that illustrates a non-limiting exampleembodiment of a method 1000 of optimizing a design of a physical deviceaccording to various aspects of the present disclosure. The method 1000is similar to the method 800 discussed above, though instead of loopingthrough multiple perturbed structural parameters to determine whether aninitial design is robust to changes in operating conditions, the method1000 uses a fabrication model as illustrated in FIG. 9 to separatelydetermine the robustness loss.

It is appreciated that method 1000 is an inverse design process that maybe accomplished by performing operations with a system (e.g., system 500of FIG. 5) to perform iterative gradient-based optimization of a lossmetric determined from a loss function that includes at least aperformance loss and a fabrication loss. In the same or otherembodiments, method 1000 may be included as instructions provided by atleast one machine-accessible storage medium (e.g., non-transitorymemory) that, when executed by a machine, will cause the machine toperform operations for generating and/or improving the design of thephotonic integrated circuit. It is further appreciated that the order inwhich some or all of the process blocks appear in method 1000 should notbe deemed limiting. Rather, one of ordinary skill in the art having thebenefit of the present disclosure will understand that some of theprocess blocks may be executed in a variety of orders not illustrated,or even in parallel.

From a start block, the method 1000 proceeds to block 1002, where aninitial design 936 of a physical device such as a photonic integratedcircuit is received. The initial design 936 is similar to the initialdesign 736 described above, and so is not described again in detail herefor the sake of brevity.

At block 1004, a fabrication model 938 is determined for analyzing arobustness loss of initial designs. As discussed above, the fabricationmodel 938 is configured to determine a robustness of various features ofinitial designs, and may be trained using machine learning techniques.For example, in some embodiments, the fabrication model 938 may becreated by generating perturbed structural parameters based on one ormore initial designs using techniques similar to those discussed abovewith respect to FIG. 7 and FIG. 8, and then using the initial structuralparameters and the perturbed structural parameters as training data fora machine learning technique including but not limited to a neuralnetwork. The machine learning technique may then automatically build thefabrication model 938 to detect which features of structural parametersare likely to introduce robustness loss in the presence of differentoperating conditions and which features of structural parameters arelikely to be robust to changes in the operating conditions. In someembodiments, the fabrication model 938 may be determined using theinitial design 936 during method 1000, while in other embodiments, thefabrication model 938 may be determined using other initial designs,separately from method 1000, or during multiple iterations of method1000.

At block 1006, a simulated environment is configured to berepresentative of the structural parameters 908 of the physical device(e.g., photonic device). Block 1008 shows mapping each of a plurality ofdistinct wavelength channels to a respective one of the plurality ofsecond communication regions. Block 1010 illustrates performing anoperational simulation of the physical device within the simulatedenvironment operating in response to one or more excitation sources todetermine a performance loss value. Other than using the structuralparameters 908 instead of perturbed structural parameters, theconfiguration of the simulated environment in block 1006, the mapping ofthe wavelength channels in block 1008, and the determination of theperformance loss value in block 1010 are similar to the actionsdescribed in block 808, block 810, and block 812 of FIG. 8, and so arenot described again here for the sake of brevity.

Block 1010 also illustrates that the operational simulation of thephysical device is also performed to determine a robustness metric. Asillustrated in FIG. 9, the structural parameters are provided to thefabrication model 938, which determines a robustness of various featuresgiven by the structural parameters, and the robustness is provided tothe perturbation model 940 along with the field values at each updateoperation. The perturbation model 940 uses the field values to determinean effect of the robustness at each update operation, thereby generatingthe robustness metric.

Block 1012 shows determining a loss metric 924 based on the performanceloss value, a fabrication loss associated with a minimum feature size,and a robustness loss associated with the robustness metric. In someembodiments the loss metric is determined via a loss function thatincludes both the performance loss value, the fabrication loss, and therobustness loss as input values. The loss metric 924 may be determinedin any suitable way, including but not limited to by performing a linearcombination of the performance loss value, the fabrication loss, and therobustness loss.

Block 1014 illustrates backpropagating the loss metric via the lossfunction through the simulated environment to determine an influence ofchanges in the structural parameters on the loss metric (i.e.,structural gradient). The loss metric is treated as an adjoint orvirtual source and is backpropagated incrementally from a final timestep to earlier time steps in a backwards simulation to determine thestructural gradient of the physical device. Block 1016 shows revising adesign of the physical device (e.g., generated a revised description) byupdating the structural parameters of the initial design 936 to adjustthe loss metric. Block 1014 and block 1016 are similar to block 820 andblock 822, and so the detailed description of these blocks is notrepeated here for the sake of brevity. The difference in block 1014 andblock 1016 is that the loss metric 924 includes the robustness lossdetermined using the fabrication model 938 and the perturbation model940. Incorporating the robustness loss into the loss metric 924 allowsthe robustness to be considered when revising the design withoutsimulating each set of perturbed structural parameters each time throughthe loop.

At decision block 1018, a determination is made regarding whether theloss metric substantially converges such that the difference between theperformance metric and the target performance metric is within athreshold range. Iterative cycles of simulating the physical device withthe excitation source selected from the plurality of distinct wavelengthchannels, backpropagating the loss metric, and revising the design byupdating the structural parameters to reduce the loss metric until theloss metric substantially converges such that the difference between theperformance metric and the target performance metric is within athreshold range. In some embodiments, the structural parameters of thedesign region of the integrated photonic circuit are revised whenperforming the cycles to cause the design region of the photonicintegrated circuit to optically separate each of the plurality ofdistinct wavelength channels from a multi-channel optical signalreceived via the first communication region and guide each of theplurality of distinct wavelength channels to the corresponding one ofthe plurality of second communication regions.

If the determination is that the loss metric has not converged, then theresult of decision block 1018 is NO, and the method 1000 returns toblock 1008 to iterate on the revised initial design 936. Otherwise, ifthe determination is that the loss metric has converged, then the resultof decision block 1018 is YES, and the method 1000 advances to block1020

Block 1020 illustrates outputting an optimized design of the physicaldevice in which the structural parameters have been updated to have thedifference between the performance metric and the target performancemetric within a threshold range while also enforcing a minimum featuresize and binarization. The method 1000 then proceeds to an end block andterminates.

In the preceding description, numerous specific details are set forth toprovide a thorough understanding of various embodiments of the presentdisclosure. One skilled in the relevant art will recognize, however,that the techniques described herein can be practiced without one ormore of the specific details, or with other methods, components,materials, etc. In other instances, well-known structures, materials, oroperations are not shown or described in detail to avoid obscuringcertain aspects.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the present invention. Thus, theappearances of the phrases “in one embodiment” or “in an embodiment” invarious places throughout this specification are not necessarily allreferring to the same embodiment. Furthermore, the particular features,structures, or characteristics may be combined in any suitable manner inone or more embodiments.

The order in which some or all of the blocks appear in each methodflowchart should not be deemed limiting. Rather, one of ordinary skillin the art having the benefit of the present disclosure will understandthat actions associated with some of the blocks may be executed in avariety of orders not illustrated, or even in parallel.

The processes explained above are described in terms of computersoftware and hardware. The techniques described may constitutemachine-executable instructions embodied within a tangible ornon-transitory machine (e.g., computer) readable storage medium, thatwhen executed by a machine will cause the machine to perform theoperations described. Additionally, the processes may be embodied withinhardware, such as an application specific integrated circuit (“ASIC”) orotherwise.

The above description of illustrated embodiments of the invention,including what is described in the Abstract, is not intended to beexhaustive or to limit the invention to the precise forms disclosed.While specific embodiments of, and examples for, the invention aredescribed herein for illustrative purposes, various modifications arepossible within the scope of the invention, as those skilled in therelevant art will recognize.

These modifications can be made to the invention in light of the abovedetailed description. The terms used in the following claims should notbe construed to limit the invention to the specific embodimentsdisclosed in the specification. Rather, the scope of the invention is tobe determined entirely by the following claims, which are to beconstrued in accordance with established doctrines of claiminterpretation.

What is claimed is:
 1. A non-transitory computer-readable medium havinglogic stored thereon that, in response to execution by at least onecomputing device, causes the at least one computing device to performactions for generating a design of a physical device, the actionscomprising: receiving an initial design of the physical device;simulating performance of the physical device using the initial designto determine a performance loss value; determining a robustness lossvalue that represents an effect of perturbations in operating conditionsduring fabrication on the performance loss value; determining a totalperformance loss value based on the performance loss value and therobustness loss value; backpropagating the total performance loss valueto determine a gradient corresponding to an influence of changes in theinitial design on the total performance loss value; and revising theinitial design of the physical device based at least in part on thegradient.
 2. The computer-readable medium of claim 1, wherein theactions further comprise determining a perturbation model forcalculating the robustness loss value.
 3. The computer-readable mediumof claim 2, wherein determining the robustness loss value thatrepresents an effect of perturbations in operating conditions duringfabrication on the performance loss value includes: providing stateswithin the physical device calculated during the simulation to theperturbation model to determine the robustness loss value.
 4. Thecomputer-readable medium of claim 2, wherein determining theperturbation model includes using at least a simulated performance of aphysical device as fabricated under each of a plurality of sets ofoperating conditions for fabrication of the physical device to determinethe perturbation model.
 5. The computer-readable medium of claim 4,wherein the actions further comprise determining the plurality of setsof operating conditions for fabrication of the physical device bystochastically sampling values for each operating condition frompredetermined ranges of values for each operating condition, or byuniformly sampling values for each operating condition and usingcombinations of the uniformly sampled values as the plurality of sets ofoperating conditions.
 6. The computer-readable medium of claim 4,wherein the actions further comprise: determining sets of operatingconditions that vary each operating condition separately; and using thesets of operating conditions with separately varied operating conditionsto determine a sensitivity toward each operating condition.
 7. Thecomputer-readable medium of claim 4, wherein the operating conditionsinclude at least one of ambient temperature, erosion, dilation,waveguide thickness, structure out of plane, sidewall angle, surfaceroughness, misalignment, optical aberrations, and materialimperfections.
 8. The computer-readable medium of claim 1, whereindetermining the total performance loss value based on the performanceloss value and the robustness loss value includes adding the robustnessloss value and the performance loss value.
 9. The computer-readablemedium of claim 1, wherein the actions further comprise repeating theactions of simulating performance of the physical device, determiningthe robustness loss value, determining the total performance loss value,backpropagating the total performance loss value, and revising theinitial design until the total performance loss value converges to aminimum.
 10. The computer-readable medium of claim 1, wherein theactions further comprise transmitting the revised initial design to afabrication system for fabrication.
 11. A system comprising at least onecomputing device configured with logic that, in response to execution bythe at least one computing device, causes the system to perform actionsfor generating a design of a physical device, the actions comprising:receiving an initial design of the physical device; simulatingperformance of the physical device using the initial design to determinea performance loss value; determining a robustness loss value thatrepresents an effect of perturbations in operating conditions duringfabrication on the performance loss value; determining a totalperformance loss value based on the performance loss value and therobustness loss value; backpropagating the total performance loss valueto determine a gradient corresponding to an influence of changes in theinitial design on the total performance loss value; and revising theinitial design of the physical device based at least in part on thegradient.
 12. The system of claim 11, wherein the actions furthercomprise determining a perturbation model for calculating the robustnessloss value.
 13. The system of claim 12, wherein determining therobustness loss value that represents an effect of perturbations inoperating conditions during fabrication on the performance loss valueincludes: providing states within the physical device calculated duringthe simulation to the perturbation model to determine the robustnessloss value.
 14. The system of claim 12, wherein determining theperturbation model includes using at least a simulated performance of aphysical device as fabricated under each of a plurality of sets ofoperating conditions for fabrication of the physical device to determinethe perturbation model.
 15. The system of claim 14, wherein the actionsfurther comprise determining the plurality of sets of operatingconditions for fabrication of the physical device by stochasticallysampling values for each operating condition from predetermined rangesof values for each operating condition, or by uniformly sampling valuesfor each operating condition and using combinations of the uniformlysampled values as the plurality of sets of operating conditions.
 16. Thesystem of claim 14, wherein the actions further comprise: determiningsets of operating conditions that vary each operating conditionseparately; and using the sets of operating conditions with separatelyvaried operating conditions to determine a sensitivity toward eachoperating condition.
 17. The system of claim 14, wherein the operatingconditions include at least one of ambient temperature, erosion,dilation, waveguide thickness, structure out of plane, sidewall angle,surface roughness, misalignment, optical aberrations, and materialimperfections.
 18. The system of claim 11, wherein determining the totalperformance loss value based on the performance loss value and therobustness loss value includes adding the robustness loss value and theperformance loss value.
 19. The system of claim 11, wherein the actionsfurther comprise repeating the actions of simulating performance of thephysical device, determining the robustness loss value, determining thetotal performance loss value, backpropagating the total performance lossvalue, and revising the initial design until the total performance lossvalue converges to a minimum.
 20. The system of claim 11, wherein theactions further comprise transmitting the revised initial design to afabrication system for fabrication.